Algebraic aspects of quadratic dynamical systems (Q2771950)

In his Ph. D. Thesis the author investigates connections between quadratic dynamical systems and certain nonassociative algebras with a multiplication defined by the 2-homogeneous r.h.s. part of the system. After some basic foundations he presents three parts: Orbital symmetries, Behaviour at Infinity, Modification by Linear Forms.NEWLINENEWLINENEWLINEThe use of special algebraic algebra properties, as existence of derivations, of idempotent or nilpotent elements or power-associativity, for the solution or reduction of the corresponding dynamical systems is discussed. With respect to many questions and to the algebraic background of such systems the topic is closely connected and influenced by the work of \textit{S. Walcher} [Algebras and differential equations, Hadronic Press, Palm Harbor, FL (1991; Zbl 0791.17002)].